Well it wouldn't do it any good. But why would you want to use 15 volts. Apart from that, battery chemistry determines how it should be charged and without that information you are on a hiding to nothing. Lithium type batteries are particularly fussy about charge regimes.

Yes, I am pretty sure you could find a way to use 15V to make 3.5V Lithium battery explode.

Assuming you don't actually want to do that, you'd need to know the specific Lithium chemistry. Each type of Lithium chemistry requires a different charge profile. Once you find out the specific chemistry (and even if it is rechargeable or not), do a google search on charging that particular type of battery. As jackrae says, they can be real fussy. Some types have built in protection circuitry and if you abuse them they will brick themselves to avoid that explosion you mentioned. At that point you can just go out and buy a new battery along with the proper charger.

If it's 3.5V then it's probably Li-ion or Li-poly. The usual charging profile for these is a constant current charge until a certain voltage is reached (the chosen voltage is between 4.05 and 4.20V), then a constant voltage charge after that. The voltage needs to be accurate to within better than 50mV.

To charge it from 15V, you would need a switching regulator and control circuit to give that charging profile. Easiest solution is to buy a ready-made one.

Formal verification of safety-critical software, software development, and electronic design and prototyping. See http://www.eschertech.com. Please do not ask for unpaid help via PM, use the forum.